MTH132-Quiz6 - equal length n a b x x k / ) (-= = . (a) [3...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: April 13, 2009 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 15 minutes. 1. [2 pts each] . Evaluate the sums. (a) = + 2 1 2 2 2 3 k k k (b) = 4 0 2 sin k k k π 2. Evaluate the sums by formulas . (a)[2 pts] = - 10 1 ) 2 ( k k (b)[2 pts] = + 6 1 ) 6 3 ( k k k 3. [2 pts each]. Suppose 2 ) ( 2 1 - = dx x f , 5 ) ( 5 1 = dx x f , 3 ) ( 5 1 - = dx x g . Use the rules to find (a) = dx x g ) (
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Page 2 10/18/2011 (b) = + 5 1 )] ( 3 ) ( 5 [ dx x g x f (c) = 2 5 ) ( dx x f 4. Let 3 2 ) ( + = x x f defined over ] 2 , 0 [ . Consider the Riemann sum: = n k k k x c f 1 ) ( . Usually, we choose
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Unformatted text preview: equal length n a b x x k / ) (-= = . (a) [3 pts]. Partition ] 2 , [ into 4 subintervals of equal length, then choose the right-hand endpoint of each subinterval ( x k a x c k k + = = ) to evaluate the Riemann sum. (b) [2 pts]. Find a formula for the Riemann sum obtained by dividing the interval into n equal subintervals. (c) [1 pt]. Find a definite integral to express the limit of the Riemann sum as n approaches infinity. (d) [bonus 2 pts]. Evaluate the limit of this Riemann sum as n approaches infinity....
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This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Quiz6 - equal length n a b x x k / ) (-= = . (a) [3...

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